Repeated Exponentiation
Just as exponentiation of natural numbers is motivated by repeated multiplication, it is possible to define an operation based on repeated exponentiation; this operation is sometimes called tetration. Iterating tetration leads to another operation, and so on. This sequence of operations is expressed by the Ackermann function and Knuth's up-arrow notation. Just as exponentiation grows faster than multiplication, which is faster growing than addition, tetration is faster growing than exponentiation. Evaluated at (3,3), the functions addition, multiplication, exponentiation, tetration yield 6, 9, 27, and 7,625,597,484,987 respectively.
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Famous quotes containing the word repeated:
““Seven years and six months!” Humpty Dumpty repeated thoughtfully. “An uncomfortable sort of age. Now if you’d asked my advice, I’d have said ‘Leave off at seven’Mbut it’s too late now.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)